I did test the Mint 12 LXDE RC and found that worked with a 4.0GB HDD as measured by Gparted or Vbox. The installer says it needs 4.2GB. More info here: viewtopic.php?f=175&t=86542&start=60#p547263In Vbox also worked down to 208MB of RAM so computers with 256MB of RAM and a shared graphic card should also work.

Edit: The installer limitation to 4.3GB can be removed by connecting a usb pen to the Eee. The disk size and pen size add up and the installer works. May work with a memory card but didn’t test that.